Purchase Solution

Isomorphic group

Not what you're looking for?

Ask Custom Question

Consider the cartesian product H=Z_2 X Z_n (as a set).Define a binary operation on H to be (i,j)*(k,l)=(i+k,(-1)^k *j+l), where i,j,k and l are vectors.

Show that H is a group under this operation, determine its order.

Let G = < a,b|a^n=1, b^2=1, abab^-1=1 >
Show that |G|<=2n.

Show that H is isomorphic to G.

See attached file

Attachments
Purchase this Solution
Solution Summary

This provides an example of proving something is a group and that it is isomorphic.

Purchase this Solution
Free BrainMass Quizzes
Probability Quiz

Some questions on probability

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

View More Free Quizzes
Related BrainMass Solutions

  • Calculations with Isomorphic Groups

    Write the octic group as a group of permutation expressed as cycle. (see attached file for chart) Please see the attachment. This solution answers questions regarding isomorphic groups.

  • Isomorphic proofs

    Answer: False Counter Example: Let , , , , then , but is not abelian and thus not isomorphic to the abelian group . This provides examples of completing proofs regarding isomorphisms.

  • Isomorphic groups

    Decide which (if any) of the following are isomorphic to which: (a) D3xS4 (b) D6xA4 (c) D4xD9 Dn=dihedral group of order 2n, An=alternating group of degree n, Sn=symmetric group of degree n GxH=internal direct product of G and H please see attached

  • Question about group theory, cardinality and isomorphic

    60709 Group theory, cardinality and isomorphic example problems I would like to know how to identify and prove the cardinality of sets and how to identify isomorphic. (See attached file for full problem description) Group Theory: a.

  • Isomorphic : Noncyclic Group Order 4

    104709 Isomorphic: Noncyclic Group Order 4 Let V be a noncyclic group of order 4. (We know that all such groups are isomorphic, one is given in example 2.96). How large is Aut(V)? To which familiar group is Aut(V) isomorphic?

  • Composition Series

    9179 Composition Series Write a composition series for the rotation group of the cube and show that it is indeed a composition series. The rotation group of the cube is isomorphic to S4 as a permutation group.

  • Permutation isomorphic

    x S2 De ne two group actions of a group G on itself as follows: (i) the action of x 2 G is left multiplication by x; (ii) the action of x 2 G is right multiplication by x􀀀1 Show that the two actions are permutation isomorphic. 1 Let theta

  • Isomorphism

    Theorem: Any 60 element group having 24 elements of order 5, 20 elements of order 3, and 15 elements of order 2 (which is exactly the group of rigid motions)is a simple group and is isomorphic to A_5.

  • Groups

    230517 Groups of Isomorphic Rational Numbers Give an example of groups H_i, K_j such that H_1xH_2 is isomorphic to K_1xK_2 and no H_i is isomorphic to any K_j. Let G be the additive group Q of rational numbers.

View More Related Solutions